14949 + Interview Questions in Maths in Class 11 Page 38 InterviewSolution

1851.	Two ships A and B are sailing away from a point O along routes such that angle AOB is always 120^(@). At a certain instance, OA = 8 KM OB = 6km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr)
Answer» `(260)/(SQRT(37))` `(260)/(37)` `(80)/(sqrt(37))` `(80)/(37)` ANSWER :A

Discussion

1852.	In triangle ABC, base BC and area of triangle D are fixed. Locus of the centroid of triangle ABC is a striaght line is
Answer» PARALLEL to SIDE BC right bisector of side BC right ANGLE of BC INCLINED at an angle `sin^(-1)(( SQRT(Delta))/(BC))` to side BC Answer :A

Discussion

1853.	If 'p' and 'q' are +ve integers, f is a function defined for +ve numbers and attains only +ve values such that f(x, f(y))=x^(p) y^(q) then p^(2)=
Answer» 2q q 3q 4q Answer :B

Discussion

1854.	Sum of the series S=t^(2) - 2^(2) + 3^(2) - 4^(2) + …... - 2002^(2) + 2003^(2) is
Answer» `2007006` `1005004` `2000506` `207006` ANSWER :A

Discussion

1855.	Find the locus of the point of intersection of the lines x=a/(m^(2)) and y=(2a)/(m), where m is a parameter.
Answer» ANSWER : `y^(2)=4AX`

Discussion

1856.	A = {1, 2, 3, 4), B = {a, b, c, d, e}, then the number of all possible constant functions from A to B is
Answer» 9 4 5 16 Answer :C

Discussion

1857.	If A is non - singular and A^(2)-5A+7I=0 then I =
Answer» `1/7A-5/7A^(-1)` `1/7A+5/7A^(-1)` `1/5A+7/5A^(-1)` `1/5A-A^(-1)` ANSWER :C

Discussion

1858.	If the percentage error in the radius of a circle is 3 then the percentage error in its area is
Answer» 6 `(3)/(2)` 2 4 Answer :A

Discussion

1859.	The sum of n terms of two arithmetic progressions are in the ratio (5n+4): (9n+ 6). Find the ratio of their 18^(th) terms
Answer» ANSWER :`(179)/(321)`

Discussion

1860.	Let coordinates of the points A and B are (5,0) and (0,7) respectively. P and Q the variable point lying on the x-axis and y-axis respectively so that PQ is always perpendicular to the line AB. The locus of the point of intersection BP and AQ is
Answer» `x^2+y^2-5x+7y =0` `x^2+y^2+5x-7y =0` `x^2+y^2+5x+7y =0` `x^2+y^2-5x-7y =0` ANSWER :B

Discussion

1861.	Obtain the equation of the parabola with given conditions: Vertex (0,0) X-axis as axis of the parabola and passes from (1, -4).
Answer» ANSWER :`y^(2) = 16X`

Discussion

1862.	Find the derivate of x^(5)(3-6x^(-9))
Answer» ANSWER :`15X^(4)+(24)/(x^(5))`

Discussion

1863.	If x^3-2x^2y^2+5x+y-5 = 0 and y(1)= 1 then
Answer» `y'(1)=4//3` `y''(1) =-4//3` `y''(1)=-8(22)/27` `y'(1) =2//3` Answer :A::C

Discussion

1864.	Find the approximate value of f(x)=(x-2)^(2)(x-3), when x=3.05
Answer» ANSWER :0.05

Discussion

1865.	If alpha + beta + gamma = 2pi, then
Answer» `TAN alpha/2 + tan beta/2 + tan gamma/2 = tan alpha/2 tan beta/2 tan gamma/2` `tan alpha/2tan beta/2 + tan beta/2 tan gamma/2 + tan gamma/2 tan alpha/2=1` `tan alpha/2 + tanbeta/2 + tan gamma/2 =-tan alpha/2 tan beta/2 tan gamma/2` `SUM tan(alpha/2) tan(beta/2)=-1` ANSWER :A

Discussion

1866.	Find from first principles the differential coefficient of sin 2x.
Answer» ANSWER :`2 COS 2X`

Discussion

1867.	The solution of 4 sin^(2) x + tan^(2) x + cosec^(2) x + cot^(2) x - 6 = 0 " is " (n in Z)
Answer» `n PI PM (pi)/(4)` `2 n pi pm (pi)/(4)` `n pi + (pi)/(3)` `n pi - (pi)/(6)` Answer :A

Discussion

1868.	The roots of the equation ax^(2)+bx+c=0 are alpha and beta. Form the quadratic equation whose roots are alpha+(1)/(beta) and beta+(1)/(alpha).
Answer» Answer :`ACX^(2)+B(c+a)X+(c+a)^(2)=0`.

Discussion

1869.	Consider the points A(2,-3,0) and B (-1,1,c) Find the distance between A and B
Answer» SOLUTION :`sqrt25+c^2`

Discussion

1870.	In triangle ABC, of r_(1)= 2r_(2)=3r_(3) Then a:bis equal :-
Answer» `4/5` `5/4` `7/4` `4/7` ANSWER :B

Discussion

1871.	Let f : R to R be a function defined by f (x + y) = f (x).f (y) and f (x) ne 0 for andy x. If f '(0) exists, show that f '(x) = f (x). F'(0) AA x in R if f '(0) = log 2 find f (x).
Answer» ANSWER :`F (X)= 2 ^(x)`

Discussion

1872.	Cos[Sin^(-1)(2cos^(2)theta-1)+Cos^(-1)(1-2sin^(2)theta)]=
Answer» 0 1 -1 `pi/2` ANSWER :A

Discussion

1873.	Letveca = 2 hati+hatj-2hatk, vecb=hati+hatj. If vecc is a vector such that veca*vecc=vecc-veca=2sqrt(2) and the angle between \|(veca xx vecb) xx vecc\| equals:
Answer» `(1)/(2)` `(3sqrt(3))/(2)` 3 `(3)/(2)` ANSWER :D

Discussion

1874.	A cricket club has 16 members, of whom only 5 can bowl . What is the probability that in a team of 11 members at least 3 bowlers are selected?
Answer» <P> ANSWER :`THEREFORE P(A) = (N(A))/(n(S)) = (3762)/(4368) = (627)/(728)`.

Discussion

1875.	Let f(x)=x^(2) and g(x)= sin x for all x in R. Then the set of all x satisfying (fogogof)(x)=(gogof)(x), where (fog)(x)=f(g(x)), is
Answer» `pm sqrt(N pi), n in {0,1,2..........}` `pm sqrt(n pi), n in {1,2,..}` `pi/2 + 2 n pi, n in {..........,-2,-1,0,1,2......}` `1N pi, n in {......, -2, -1, 0, 1, 2, ........}` ANSWER :A

Discussion

1876.	Prove that the functions sin x, cos x are continuous on R
Answer» ANSWER :there is no POINT of discontinouity

Discussion

1877.	If y=(x+sqrt(x^2-a^2))^n then (x^2-a^2)((dy)/(dx))^2=
Answer» `n^2y` `-n^2y` `ny^2` `n^2y^2` ANSWER :D

Discussion

1878.	(ax+b)(cx+d)^(2)
Answer» ANSWER :`2C(ax+b)(cx+d)+a(cx+d)^(2)`

Discussion

1879.	Find the coordinates of the vertex and the focus of the parabola y^(2)=4(x+y).
Answer» ANSWER :`y^(2)=4x+4y=>(y-2)^(2)=4(x+1)` vertex `(-1,2)`, FOCUS `(0,2)`

Discussion

1880.	Maximum value of 'r' such that (e^(2))/(r^(2))=(a^(2))/(sin^(2)theta)+(b^(2))/(cos^(2)theta) where c,a,b are constants is
Answer» `(C)/(a+B)` `(c)/(a-b)` `(a^(2)+b^(2))/(c^(2))` `(c^(2))/(a^(2)+b^(2))` ANSWER :A

Discussion

1881.	Ifr_1= r_2 = r_3then triangleis
Answer» RIGHT ANGLED ISOSCELES Equilateral Scalane ANSWER :C

Discussion

1882.	(d)/(dx)(sin180^(@))=………
Answer» COS `18^(@)` `-SIN18^(@)` `-xos18^(@)` 0 Answer :D

Discussion

1883.	There are 5 red balls and x black balls . If twoballs are drawn at random , probability that theballsdrawnare red is (5)/(14), findthe value of x?
Answer» 9 12 3 6 Answer :C

Discussion

1884.	If a,b,c are in G.P and A.M of a and b is x and A.M. of b and c is y then…….
Answer» `(1)/(X) + (1)/(y)=2` `(1)/(x) + (1)/(y) = (1)/(2)` `(1)/(x) + (1)/(y) = (2)/(a)` `(1)/(x) + (1)/(y) = (2)/(B)` ANSWER :D

Discussion

1885.	Find the angle between the lines vec(AB) and vec(BC) where (i) A(0,-1),B(2,1),C(0,3) (ii) A(0,0),B(sqrt(3),3),C(-sqrt(3),3)
Answer» ANSWER :(i) `90^(@)` (II) `60^(@)`

Discussion

1886.	The variable line x//a+y//b=1 is such that a+b=10. The locus of the midpoint of the portion of the line intercepted between theaxes is
Answer» `x+y=10` `10x+5y=1` `x+y=5` `5x+10y=1` ANSWER :C

Discussion

1887.	Find the derivative of the w.r.to x. (sin x ) ^(x) + x ^( sin x)
Answer» ANSWER :`(SIN X ) /(x)`

Discussion

1888.	Equation to the locus of points which are equal distance from the points (1, -3, 4), (1, 3, 4) is
Answer» XY = 0 y = 0 z = 0 X = 0 Answer :b

Discussion

1889.	Showthat the set of all points such that the difference of their distances from (4,0) and (-4, 0) is always equal to 2 represent a hyperbola.
Answer» Answer :`15X^(2) - y^(2) = 15` which represents hyperbola.

Discussion

1890.	If the number of the elements of ordered pairs A xx A is 16 and (a, a) (b, a) (a,c) (d,d) are elements of A xx A then find A
Answer» ANSWER :A= {a,B,C,d}

Discussion

1891.	If 20 lines are drawn in a plane such that no two of them are paralled and no there are concurrent, in how many points will thay intersect each other ?
Answer» ANSWER :190

Discussion

1892.	The pair of lines 2x^(2)+3xy+5y^(2)=0 and 4x^(2)+21xy+25y^(2)=0 are
Answer» perpendicular EQUALLY INCLINED to axes equally inclined to each other NONE Answer :C

Discussion

1893.	A room has 3 lamps . From a collection of 10 light bulbs of which 6 are no good , a person selects 3 at random andputs them in a socket . What is the probability , that he will have light ?
Answer» ANSWER :`(5)/(6)`

Discussion

1894.	For every natural number n, 3^(2n+2) - 8n -9 is divisible by
Answer» 16 128 256 512 Answer :A

Discussion

1895.	What will be the value of m and c if the straight line y=mx+c passes through the points (3, -4) and (-1, 2) ?
Answer» ANSWER : `m=(-3)/(2), c=1/(2)`

Discussion

1896.	IF tan ^(2) alpha tan ^(2) beta + tan ^(2) beta tan ^(2) gamma + tan ^(2) gamma tan ^(2 ) alpha + 2 tan ^(2) alpha + sin ^(2) beta + sin ^(2)gamma is
Answer» 0 `-1` 1 2 Answer :C

Discussion

1897.	A function f(x) is definedas f(x)= {:{(1," when " x != 0),(2," when " x = 0 ):}does the Limit of f(x) as x to 0exist ? Explain your answer .
Answer» ANSWER :` :.Lim_(x to 0 ) ` f(x)exists and its valueis 1 .

Discussion

1898.	Which is not the measur of central tendency ?
Answer» MEAN MEDIAN MODE RANGE ANSWER :D

Discussion

1899.	Write the converse of each of the following statements If it is raining, then there are clouds in the sky :
Answer» ANSWER :If there are CLOUDS in the SKY, then it is RAINING.

Discussion

1900.	Insert five numbers between 8 and 26 such that the resulting sequence is in AP.
Answer» ANSWER :11,14,17,20 and 23

Discussion

Explore topic-wise InterviewSolutions in .

In triangle ABC, base BC and area of triangle D are fixed. Locus of the centroid of triangle ABC is a striaght line is

If 'p' and 'q' are +ve integers, f is a function defined for +ve numbers and attains only +ve values such that f(x, f(y))=x^(p) y^(q) then p^(2)=

Sum of the series S=t^(2) - 2^(2) + 3^(2) - 4^(2) + …... - 2002^(2) + 2003^(2) is

Find the locus of the point of intersection of the lines x=a/(m^(2)) and y=(2a)/(m), where m is a parameter.

A = {1, 2, 3, 4), B = {a, b, c, d, e}, then the number of all possible constant functions from A to B is

If A is non - singular and A^(2)-5A+7I=0 then I =

If the percentage error in the radius of a circle is 3 then the percentage error in its area is

The sum of n terms of two arithmetic progressions are in the ratio (5n+4): (9n+ 6). Find the ratio of their 18^(th) terms

Let coordinates of the points A and B are (5,0) and (0,7) respectively. P and Q the variable point lying on the x-axis and y-axis respectively so that PQ is always perpendicular to the line AB. The locus of the point of intersection BP and AQ is

Obtain the equation of the parabola with given conditions: Vertex (0,0) X-axis as axis of the parabola and passes from (1, -4).

Find the derivate of x^(5)(3-6x^(-9))

If x^3-2x^2y^2+5x+y-5 = 0 and y(1)= 1 then

Find the approximate value of f(x)=(x-2)^(2)(x-3), when x=3.05

If alpha + beta + gamma = 2pi, then

Find from first principles the differential coefficient of sin 2x.

The solution of 4 sin^(2) x + tan^(2) x + cosec^(2) x + cot^(2) x - 6 = 0 " is " (n in Z)

The roots of the equation ax^(2)+bx+c=0 are alpha and beta. Form the quadratic equation whose roots are alpha+(1)/(beta) and beta+(1)/(alpha).

Consider the points A(2,-3,0) and B (-1,1,c) Find the distance between A and B

In triangle ABC, of r_(1)= 2r_(2)=3r_(3) Then a:bis equal :-

Let f : R to R be a function defined by f (x + y) = f (x).f (y) and f (x) ne 0 for andy x. If f '(0) exists, show that f '(x) = f (x). F'(0) AA x in R if f '(0) = log 2 find f (x).

Cos[Sin^(-1)(2cos^(2)theta-1)+Cos^(-1)(1-2sin^(2)theta)]=

Letveca = 2 hati+hatj-2hatk, vecb=hati+hatj. If vecc is a vector such that veca*vecc=vecc-veca=2sqrt(2) and the angle between |(veca xx vecb) xx vecc| equals:

A cricket club has 16 members, of whom only 5 can bowl . What is the probability that in a team of 11 members at least 3 bowlers are selected?

Let f(x)=x^(2) and g(x)= sin x for all x in R. Then the set of all x satisfying (fogogof)(x)=(gogof)(x), where (fog)(x)=f(g(x)), is

Prove that the functions sin x, cos x are continuous on R

If y=(x+sqrt(x^2-a^2))^n then (x^2-a^2)((dy)/(dx))^2=

(ax+b)(cx+d)^(2)

Find the coordinates of the vertex and the focus of the parabola y^(2)=4(x+y).

Maximum value of 'r' such that (e^(2))/(r^(2))=(a^(2))/(sin^(2)theta)+(b^(2))/(cos^(2)theta) where c,a,b are constants is

Ifr_1= r_2 = r_3then triangleis

(d)/(dx)(sin180^(@))=………

There are 5 red balls and x black balls . If twoballs are drawn at random , probability that theballsdrawnare red is (5)/(14), findthe value of x?

If a,b,c are in G.P and A.M of a and b is x and A.M. of b and c is y then…….

Find the angle between the lines vec(AB) and vec(BC) where (i) A(0,-1),B(2,1),C(0,3) (ii) A(0,0),B(sqrt(3),3),C(-sqrt(3),3)

The variable line x//a+y//b=1 is such that a+b=10. The locus of the midpoint of the portion of the line intercepted between theaxes is

Find the derivative of the w.r.to x. (sin x ) ^(x) + x ^( sin x)

Equation to the locus of points which are equal distance from the points (1, -3, 4), (1, 3, 4) is

Showthat the set of all points such that the difference of their distances from (4,0) and (-4, 0) is always equal to 2 represent a hyperbola.

If the number of the elements of ordered pairs A xx A is 16 and (a, a) (b, a) (a,c) (d,d) are elements of A xx A then find A

If 20 lines are drawn in a plane such that no two of them are paralled and no there are concurrent, in how many points will thay intersect each other ?

The pair of lines 2x^(2)+3xy+5y^(2)=0 and 4x^(2)+21xy+25y^(2)=0 are

A room has 3 lamps . From a collection of 10 light bulbs of which 6 are no good , a person selects 3 at random andputs them in a socket . What is the probability , that he will have light ?

For every natural number n, 3^(2n+2) - 8n -9 is divisible by

What will be the value of m and c if the straight line y=mx+c passes through the points (3, -4) and (-1, 2) ?

IF tan ^(2) alpha tan ^(2) beta + tan ^(2) beta tan ^(2) gamma + tan ^(2) gamma tan ^(2 ) alpha + 2 tan ^(2) alpha + sin ^(2) beta + sin ^(2)gamma is

A function f(x) is definedas f(x)= {:{(1," when " x != 0),(2," when " x = 0 ):}does the Limit of f(x) as x to 0exist ? Explain your answer .

Which is not the measur of central tendency ?

Write the converse of each of the following statements If it is raining, then there are clouds in the sky :

Insert five numbers between 8 and 26 such that the resulting sequence is in AP.